DOI 10.4010/2016.947 ISSN 2321 3361 © 2016 IJESC Research Article Volume 6 Issue No. 4 Harmonics: What are they? What do they do? Echegini Ngozi Silas1, Madubuike, Fidelia Ifeyinwa2 Mechatronic Instructor/Researcher at Skill ‘G’ Nigeria Limited, Abuja Nigeria1 Electronics Engineering Instructor/Researcher at Skill 'G' Nigeria Limited, Abuja Nigeria2 silasngoziechegini@gmail.com1, delia4nneoma@gmail.com2 Abstract: Harmonics are everywhere just as the air is everywhere. As long as there is some form of wave signal characterized by a certain frequency, there is bound to be a harmonic signal. The phenomenon is a vital one with respect to electronics, electromagnetism, electric fields and various forms of wave. A harmonic is a signal or wave whose frequency is a whole number multiple of the frequency of some reference signal or wave. For instance, if the frequency of a reference signal is ‘f’, then the harmonics will be in the order (f, 2f, 3f, …. And so on). Thus, the first harmonic is usually the same as the frequency of the reference signal and we have the second, third, etc. harmonic. Signals occurring at frequencies of 2 f , 4 f , 6 f , etc. are called even harmonics; the signals at frequencies of 3 f , 5 f , 7 f , etc. are called odd harmonics. A signal can, in theory, have infinitely many harmonics. The term can also refer to the ratio of the frequency of such a signal or wave to the frequency of the reference signal or wave. If ‘f’ represent the fundamental frequency of an AC signal, electromagnetic field or sound wave, this frequency, usually expressed in hertz is the frequency at which most of the energy is contained, or at which the signal is defined to occur. If the signal is displayed on an oscilloscope, the waveform will appear to repeat at a rate corresponding to f Hz. 1. INTRODUCTION: Most signals contain energy at harmonic frequencies in addition to the energy at the fundamental frequency. A signal will be a perfect sine wave if all the energy in that signal is contained at the fundamental frequency. On the contrary, the event where the signal is not a perfect sine wave implies that some energy is contained in the harmonics. Some waveforms contain large amounts of energy at harmonic frequencies. Typical are square waves, saw-tooth waves, and triangular waves. 2. What are harmonics? Harmonics allow for the representation of any periodic waveform. In fact, according to Fourier’s theorem, any periodic function of a period T may be represented as a summation of: A sinusoid with the same period T; Some sinusoids with the same frequency as whole multiples of the fundamental; A possible continuous component, if the function has an average value not null in the period. Thus, we can say that harmonics are nothing less than the components of a distorted waveform and their use allows us to analyze any periodic nonsinusoidal waveform through different sinusoidal waveform components. International Journal of Engineering Science and Computing, April 2016 The equation for the harmonic expansion of a periodic function is presented below: Where: – Value of the DC component, generally zero and considered as such hereinafter, – rms value of the nth harmonic, ω – angular frequency of the fundamental frequency, – displacement of the harmonic component at t = 0. Any harmonic with frequency corresponding to the period of the original waveform is called fundamental and the harmonic with frequency equal to “n” times that of the fundamental is called harmonic component of order “n”. A perfectly sinusoidal waveform complying with Fourier’s theorem does not present harmonic components of order different from the fundamental one. Therefore, it is understandable how there are no harmonics in an electrical system when the waveforms of current and voltage are sinusoidal. On the contrary, the presence of harmonics in an electrical system is an index of the distortion of the voltage or current waveform and this implies such a distribution of the electric power that malfunctioning of equipment and protective devices can be caused. 4120 http://ijesc.org/ This nonsinusoidal waveform can be deconstructed into harmonics. If the network impedances are very low, the voltage distortion resulting from a harmonic current is low too and rarely above the pollution level already present in the network. As a consequence, the voltage can remain practically sinusoidal also in the presence of current harmonics. To function properly, many electronic devices need a definite current waveform and thus they have to ’cut’ the sinusoidal waveform so as to change its rms value or to get a direct current from an alternate value. In these cases the current on the line has a nonsinusoidal curve. Figure (1) is a graphical representation of this concept. 3. How harmonics are generated: Harmonics are generated by non-linear loads. A load is said to be non-linear when the current it draws does not have the same wave form as the supply voltage. Devices comprising power electronics circuits are typical non-linear loads. Such loads are increasingly frequent and their percentage in overall electrical consumption is growing steadily. When we apply a sinusoidal voltage to a load of this type, we shall obtain a current with non-sinusoidal waveform. The diagram of Figure (2) illustrates an example of nonsinusoidal current waveform due to a nonlinear load: Figure 2 – Left: Linear load waveform; Right: Non-linear load waveform International Journal of Engineering Science and Computing, April 2016 3.1 Equipment generating harmonics include: Personal computer Fluorescent lamps Static converters Continuity groups Variable speed drives Welders In general, waveform distortion is due to the presence of bridge rectifiers (inside of these equipment), whose semiconductor devices carry the current only for a fraction of the whole period, thus originating discontinuous curves with the consequent introduction of numerous harmonics. Also transformers can be a cause of harmonic pollution. In fact, by applying a perfectly sinusoidal voltage to a transformer, it results into a sinusoidal magnetizing flux. However, due to the phenomenon of the magnetic saturation of iron, the magnetizing current shall not be sinusoidal. Figure 3 shows a graphic representation of this phenomenon: Phenomenon of the magnetic saturation of transformer iron The resultant waveform of the magnetizing current contains numerous harmonics, the greatest of which is the third one. However, it should be noted that the magnetizing current is generally a little percentage of the rated current of the 4121 http://ijesc.org/ transformer and the distortion effect becomes more and more negligible the most loaded the transformer results to be. 3.1.1 The main problems caused by harmonic currents are: i. overloading of neutrals ii. Increase of losses in the transformers iii. Increase of skin effect 3.1.2 The main effects of the harmonics voltages are: iv. voltage distortion v. disturbances in the torque of induction motors i. Overloading of neutrals: In a three phase symmetric and balanced system with neutral, the waveforms between the phases are shifted by a 120° phase angle so that, when the phases are equally loaded, the current in the neutral is zero. The presence of unbalanced loads (phase-to-phase, phase-toneutral etc.) allows the flowing of an unbalanced current in the neutral The same is true also for the harmonics multiple of three (even and odd, although actually the odd ones are more common). ii. Increase of losses in the transformers The effects of harmonics inside the transformers involve mainly three aspects: a. Increase of iron losses (or no-load losses) b. Increase of copper losses c. Presence of harmonics circulating in the windings The iron losses are due to the hysteresis phenomenon and to the losses caused by eddy currents. The losses due to hysteresis are proportional to the frequency, whereas the losses due to eddy currents depend on the square of the frequency. Figure (4) – Unbalanced system of currents Figure 4 above shows an unbalanced system of currents (phase 3 with a load 30% higher than the other two phases), and the current resultant in the neutral is highlighted in red. Under these circumstances, the Standards allow the neutral conductor to be dimensioned with a cross section smaller than the phase conductors. Although the currents at fundamental frequency in the three phases cancel each other out, the components of the third harmonic, having a period equal to a third of the fundamental, that is equal to the phase shift between the phases (see Figure 5 below), are reciprocally in phase and consequently they sum in the neutral conductor adding themselves to the normal unbalance currents. International Journal of Engineering Science and Computing, April 2016 Figure 5 – Fundamental harmonic and 3rd harmonic The copper losses correspond to the power dissipated by Joule effect in the transformer windings. As the frequency 4122 http://ijesc.org/ rises (starting from 350 Hz) the current tends to thicken on the surface of the conductors (skin effect). Under these circumstances, the conductors offer a smaller cross section to the current flow, since the losses by Joule effect increase. These two first aspects affect the overheating which sometimes causes a derating of the transformer. Harmonic distortion is present to some degree on all power systems. Fundamentally, one needs to control harmonics only when they become a problem. Harmonic distortion is not a new phenomenon on power systems. The third aspect is relevant to the effects of the triple-N harmonics (homopolar harmonics) on the transformer windings. In case of delta windings, the harmonics flow through the windings and do not propagate upstream towards the network since they are all in phase. The delta windings therefore represent a barrier for triple-N harmonics, but it is necessary to pay particular attention to this type of harmonic components for a correct dimensioning of the transformer. iii. Increase of skin effect When the frequency rises, the current tends to flow on the outer surface of a conductor. This phenomenon is known as skin effect and is more pronounced at high frequencies. At 50 Hz power supply frequency, skin effect is negligible, but above 350 Hz, which corresponds to the 7th harmonic, the cross section for the current flow reduces, thus increasing the resistance and causing additional losses and heating. In the presence of high-order harmonics, it is necessary to take skin effect into account, because it affects the life of cables. In order to overcome this problem, it is possible to use multiple conductor cables or bus-bar systems formed by more elementary isolated conductors. iv. Voltage distortion The distorted load current drawn by the nonlinear load causes a distorted voltage drop in the cable impedance. The resultant distorted voltage waveform is applied to all other loads connected to the same circuit, causing harmonic currents to flow in them, even if they are linear loads. The solution consists in separating the circuits which supply harmonic generating loads from those supplying loads sensitive to harmonics. v. Disturbances in the torque of induction motors Harmonic voltage distortion causes increased eddy current losses in the motors, in the same way as seen for transformers. The additional losses are due to the generation of harmonic fields in the stator, each of which is trying to rotate the motor at a different speed, both forwards (1st, 4th, 7th, …) as well as backwards (2nd, 5th, 8th, …). High frequency currents induced in the rotor further increase losses. 4. Principles of controlling harmonics i. Harmonic distortion is caused by nonlinear devices in the power system. A nonlinear device is one in which the current is not proportional to the applied voltage. International Journal of Engineering Science and Computing, April 2016 Figure (6) - Variation of the voltage THD over a 1-week period 4.1 There are three common causes of harmonic problems: a. The source of harmonic currents is too great. b. The path in which the currents flow is too long (electrically), resulting in either high voltage distortion or telephone interference. c. The response of the system magnifies one or more harmonics to a greater degree than can be tolerated. When a problem occurs, the basic options for controlling harmonics are: a. Reduce the harmonic currents produced by the load. b. Add filters to siphon the harmonic currents off the system, block the currents from entering the system, or supply the harmonic currents locally. c. Modify the frequency response of the system by filters, inductors, or capacitors. Reducing harmonic currents in loads There is often little that can be done with existing load equipment to significantly reduce the amount of harmonic current it is producing unless it is being mishandled. While an overexcited transformer can be brought back into normal operation by lowering the applied voltage to the correct range, arcing devices and most electronic power converters are locked into their designed characteristics. Pulse Width Modulator drives that charge the dc bus capacitor directly from the line without any intentional impedance are one exception to this. Adding a line reactor or transformer in series will significantly reduce harmonics, as well as provide transient protection benefits. Transformer connections can be employed to reduce harmonic currents in three-phase systems. Phase-shifting 4123 http://ijesc.org/ half of the 6-pulse power converters in a plant load by 30° can approximate the benefits of 12- pulse loads by dramatically reducing the fifth and seventh harmonics. Delta-connected transformers can block the flow of zerosequence harmonics (typically triplens) from the line. Zigzag and grounding transformers can shunt the triplens off the line. Purchasing specifications can go a long way toward preventing harmonic problems by penalizing bids from vendors with high harmonic content. This is particularly important for such loads as high-efficiency lighting. ii. Filtering The shunt filter works by short-circuiting harmonic currents as close to the source of distortion as practical. This keeps the currents out of the supply system. This is the most common type of filtering applied because of economics and because it also tends to correct the load power factor as well as remove the harmonic current. e. Remove the capacitor and simply accept the higher losses, lower voltage, and power factor penalty. If technically feasible, this is occasionally the best economic choice. 5. And now, how do we get rid of Harmonics? A load that is purely resistive has the same wave shapes for voltage and current. Both are normally pure sinusoids. Most induction motors fed directly from AC mains also behave in a similar manner except that they draw some reactive load as well. The current waveform is still sinusoidal (see Figure 7). However, the current waveform gets distorted when power electronic devices are introduced in the system to control the speed of motors. These devices chop off part of the AC waveform using thyristors or power transistors, which are used as static switches. Another approach is to apply a series filter that blocks the harmonic currents. This is a parallel-tuned circuit that offers a high impedance to the harmonic current. It is not often used because it is difficult to insulate and the load voltage is much distorted. One common application is in the neutral of a grounded-wye capacitor to block the flow of triple harmonics while still retaining a good ground at fundamental frequency. Active filters work by electronically supplying the harmonic component of the current into a nonlinear load. Modifying the system frequency response 4.2 There are a number of methods to modify adverse system responses to harmonics: a. Add a shunt filter. Not only does this shunt a troublesome harmonic current off the system, but it completely changes the system response, most often, but not always, for the better. b. Add a reactor to detune the system. Harmful resonances generally occur between the system inductance and shunt power factor correction capacitors. The reactor must be added between the capacitor and the supply system source. One method is to simply put a reactor in series with the capacitor to move the system resonance without actually tuning the capacitor to create a filter. Another is to add reactance in the line. c. Change the capacitor size. This is often one of the least expensive options for both utilities and industrial customers. d. Move a capacitor to a point on the system with a different short-circuit impedance or higher losses. This is also an option for utilities when a new bank causes telephone interference—moving the bank to another branch of the feeder may very well resolve the problem. This is frequently not an option for industrial users because the capacitor cannot be moved far enough to make a difference. International Journal of Engineering Science and Computing, April 2016 Figure (7) – Voltage and current waveforms of an induction motor Such altered waveforms may be mathematically analyzed using Fourier transforms as a combination of vectors of the power frequency (50/60 Hz) and others whose frequency is a multiple of the power frequency. The power frequency component is called the fundamental and higher multiples are called harmonics. It should be remembered that all electrical generators produce only voltage at fundamental frequency. But there has to be a source if a harmonic current has to flow. It is therefore construed theoretically that all harmonicproducing loads are current sources of harmonics. These sources drive harmonic currents through the rest of the system consisting of the source as well as other loads connected to it. These currents flowing through the different impedances of the system appear as harmonic voltages. It is usual for the voltage waveform of such a system to appear distorted. Also, the harmonic currents flowing through the other loads of the system give rise to several abnormalities (refer Table 1 below). 4124 http://ijesc.org/ Table 1 – Effects harmonics have on different system components EQUIPMENT EFFECTS OF HARMONICS Amplify harmonics on electrical Capacitors distribution system. Phase and neutral conductors Electrical wiring undersized. Transferring capability and operation Engine generators disrupted. May fail prematurely due to fifth Induction motors harmonic Metering Inaccurate measurement of power Over current Breaker and fuse nuisance tripping protection Sensitive electronic Voltage drop between neutral and earth loads Transformers Decreased efficiency and overheating Uninterruptible Line and load interaction power systems An example how shunt filters function: Let us see how these shunt filters function. We can use a computer to show what happens as harmonics are filtered from a distorted wave. The example chosen is a 120° square wave current with a 10°commutation time; a typical line current waveform for a DC motor drive and for many AC drives. Here is the square wave before any filtering. The distortion factor is 26% not too pretty a waveform (Figure 8a). Now let us take out the fifth harmonic. This may not look a whole lot better, but the distortion factor is down from 26 to 18%, so things are improving (Figure 8b). Now let us take out the seventh as well. Things are actually looking better now. We can see the sine wave starting to emerge. Distortion factor is down to 11% (Figure 8c). Next, we take out the eleventh. Still no beauty queen, but the distortion factor is now only 8% (Figure 8d). Let us add in the final element and remove the thirteenth harmonic. This is our final current waveform (Figure 8e). The distortion factor is 6%, so we are putting a reasonable current into the utility. Of course, the significance of this current waveform to the voltage distortion would depend on the source impedance and the current level. Higher-frequency harmonics can be propagated by the power conductors acting as antennae and appear as induced noise voltages in nearby signal circuits. International Journal of Engineering Science and Computing, April 2016 Figure (8) – Reduction of harmonics by filters 6. SUMMARY It is not possible to prevent harmonic currents altogether. But they can be prevented from flowing through the entire system by providing a separate low-impedance path for them. This is done by the use of adequately rated series tuned circuits consisting of a reactor and capacitor, which have equal impedance at a specific harmonic frequency. Several such tuned banks (one for each harmonic frequency) will be needed to totally divert all harmonics away from the system. However, for practical reasons, only a few of the lower order harmonics with larger magnitudes are filtered out, which is adequate to provide substantial reduction of harmonic content. Figure 2 shows how a filter might remove the highfrequency components and how the wave shape might appear as the removal takes place. 4125 http://ijesc.org/ Reference: [1] G.T. Heydt, W.M. Grady and D. Xia. "Harmonic Power Flow Studies", Theoretical Basis, EPRI EL-3300, project 1764-7, Electric Power Research Institute, Palo Alto, CA, Vol. 1, 1983. [2] Cyhharmog. Harmonic Analysis by Cyme International Inc., 1485 Roberval, Suite 204, St. Bruno, Quebec, Canada. [3] Fang Zheng Peng, Hirofumi Akagi and Akira Nabae. "A New Approach to Harmonic Compensation in Power Systems- A Combined System of Shunt Passive and Series Active Filters", IEEE Transactions on Industry Applications, Vol/Issue: 26(6), 1990. [4] Hideaki Fujita and Hirofumi Akagi. "The Unified Quality Conditioner: The Integration of Series- and ShuntActive Filters", IEEE Transactions on Power Electronics, Vol/Issue: 13(2), 1998. [5] IEEE Recommended Practices and Requirements for Harmonics Control in Electric Power Systems, IEEE Std. 519, 1992. [6] M.M. Swamy, “Passive Harmonic Filter Systems for Variable Frequency Drives,” U.S.Patent no: 5,444,609, Aug. 1995. S. Bhattacharya, D. Divan, “Active Filter Solutions for Utility Interface of Industrial Loads,” Conf. Proc. 1996, Power Electronics, Drives and Energy Systems for Industrial Growth, vol. 2, Jan. 1996, pp.1078 [7] R. Dwyer, H.V. Nguyen, S.G. Ashomre, “C Filters WideBandwidth Harmonics Attenuation with Low Losses,” Power Engineering Society Winter Meeting, 2000, vol.4, pp. 2955-2960. [8] K. Lin, M. Lin, T. Lin, ”An Advanced Computer Code for Single-Tuned Harmonic Filter Design,” IEEE Trans. on Industry Applications, vol. 34, no. 4,Jul./Aug. 1998, pp.640648. [9] G. Vijayaraghavan, Mark Brown, Malcolm Barnes “Practical Grounding, Bonding, Shielding and Surge Protection [10] Electrical Engineering Portal, “Electrical installation HandBook (Protection, Control and Electrical Devices) International Journal of Engineering Science and Computing, April 2016 4126 http://ijesc.org/